Answer:
[tex]\frac{x^2}{400}+\frac{y^2}{625}=1[/tex]
Step-by-step explanation:
The equation of an ellipse that has its center at the origin is given by the formula:
[tex]\frac{x^2}{b^2}+\frac{y^2}{a^2}=1[/tex]
The given ellipse is 50 units high.
This means that length of the major axis is 50.
[tex]2a=50[/tex]
[tex]2\implies a=25[/tex]
The ellipse is 40 units wide.
[tex]2b=40[/tex]
[tex]\implies b=20[/tex]
We substitute these values into the formula to get:
[tex]\frac{x^2}{20^2}+\frac{y^2}{25^2}=1[/tex]
[tex]\frac{x^2}{400}+\frac{y^2}{625}=1[/tex]
